The median- graphical method -progression , Mathematics

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The median

- it is a statistical value which is usually located at the center of a given set of data that has been organized in the order of size or magnitude as illustrating, consider the set 14, 17, 9, 8, 20, 32, 18, 14.5, 13. While the data is ordered it will be 8, 9, 13, 14, 14.5, 17, 18, 20, 32

The middle number or median is 14.5

-  The significance of the median lies in the fact that it divides the data into two equivalent halves. The number of observations above and below the median is equal.

-   In order to find out the value of the median from grouped data. While data is grouped the median may be determined by utilizing the given methods.

 

i.  Graphical method by using the cumulative frequency curve or ogive

ii.  The formula

Illustration

Referring to the table which is given below; determine the median by using the methods above

IQ

No of resid

UCB

Cumulative Frequency

0 - 20

6

20

6

20 - 40

18

40

24

40 - 60

32

60

56

60 - 80

48

80

104

80 - 100

27

100

131

100 - 120

13

120

144

120 - 140

2

140

146

 

                               360_The median- graphical method -Progression.png

Hence the position of the median is= (n + 1)/2

= (146 + 1)/2

ii. Computation

The formula utilized is

                                              2429_The median- graphical method -Progression 1.png

Whereas L = Lower class boundary of the class having the median

            N = No of observations

            Cfo= cfbm = Cumulative frequency of the class before that having the median

            F1 fmc = Frequency of the class having the median

 

                                         1337_The median- graphical method -Progression 2.png

= 60 + ((73.5 - 56)/48) * 20

= 60 + 7.29

= 67.29


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